Finite Group Databasebeta

← #30606276

Subgroups — #30606276

Order 15616.

782 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 782 conjugacy classes of subgroups — too many to draw. Only its 142 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#410C212yesmaximal
2#21460908C212yesmaximal, complemented
3#21460907C212yesmaximal, complemented
4#408×D61C211yesmaximal, characteristic
5C2×#14519856—22no—
6#16840743—22no—
7#16840742C414yescomplemented
8#16840741—22no—
9#16840741C2214yes—
10D61⋊#99—22no—
11D61⋊#99C414yescomplemented
12C2×#41×D61C2211yescharacteristic
13C2×M16×D61C411yescharacteristic, complemented
14C22×C8×D61C411yescharacteristic, complemented
15#16839730C2211yescharacteristic
16#16839729C411yescharacteristic, complemented
17#16839728C2211yescharacteristic
18#16839727—22no—
19C22⋊C8×D61—22no—
20C61×#408C411yescharacteristic, complemented
21#14519856—24no—
22#14519856—24no—
23#14519856—42no—
24#14519856—42no—
25C2×C4⋊#6923—42no—
26C2×C22⋊#6923—24no—
27C2×C4×#6923—42no—
28#14519836—24no—
29#14519836—24no—
30#14519835—24no—
31#14519835C2×C418yescomplemented
32C2×#11758226D411yescharacteristic
33C2×#11758222D412yes—
34C2×#11758222C2311yescharacteristic
35C2×#11758224C2×C412yes—
36C2×#11758224Q811yescharacteristic
37#41×D61—41no—
38#41×D61—41no—
39#41×D61—41no—
40#41×D61—41no—
41C2×Q8×D61Q811yescharacteristic
42C2×D4×D61C2×C412yes—
43C2×D4×D61D411yescharacteristic
44C22×C4×D61C2×C411yescharacteristic
45C22×C4×D61D412yes—
46C2×#11758194C2×C411yescharacteristic, complemented
47C2×#11758189—21no—
48M16×D61—41no—
49M16×D61—41no—
50C22×#92418C2×C411yescharacteristic, complemented
51C2×C8×D61—21no—
52C2×C8×D61—21no—
53C2×C8×D61—21no—
54C2×C8×D61—41no—
55C2×C8×D61—41no—
56C22⋊#92418—22no—
57#14519689—22no—
58#14519689—22no—
59C2×#41×C61C2×C411yescharacteristic
60C2×M16×C61C2×C411yescharacteristic, complemented
61C22×C8×C61C2×C411yescharacteristic, complemented
62C22⋊C8×C61—22no—
63C23×D61C4211yescharacteristic
64C23×D61C22⋊C412yes—
65C22×#6923—44no—
66#41×C61—41no—
67#41×C61—41no—
68C2×Q8×C61C4⋊C411yescharacteristic
69C2×D4×C61C4212yes—
70C2×D4×C61C4⋊C411yescharacteristic
71C22×C4×C61C22⋊C412yes—
72C22×C4×C61C22×C411yescharacteristic
73C2×C22⋊D61C22⋊C412yes—
74C2×C22⋊D61C4⋊C412yes—
75C2×C22⋊D61C22×C412yes—
76C22×Dic61C4211yescharacteristic
77C22×Dic61C4⋊C412yes—
78#11758226—41no—
79#11758226—41no—
80Q8×D61—41no—
81Q8×D61—41no—
82#11758224—42no—
83#11758224—42no—
84#11758224—41no—
85#11758224—41no—
86D4×D61—42no—
87D4×D61—42no—
88D4×D61—41no—
89D4×D61—41no—
90#11758222—42no—
91#11758222—42no—
92#11758222—41no—
93#11758222—41no—
94C2×D244C22⋊C412yes—
95C2×D244C2×D411yescharacteristic
96C2×C4×D61—21no—
97C2×C4×D61—21no—
98C2×C4×D61—21no—
99C2×C4×D61—21no—
100C2×C4×D61—22no—
101C2×C4×D61—22no—
102C2×C4×D61—22no—
103C2×C4×D61—22no—
104C2×C4×D61C22⋊C412yes—
105C2×C4×D61C22⋊C411yescharacteristic
106C2×C4×D61C22⋊C411yescharacteristic
107C2×C4×D61C4⋊C411yescharacteristic
108C2×C4×D61C4⋊C411yescharacteristic
109C2×C4×D61C4⋊C412yes—
110C2×C4×D61C2×D412yes—
111C2×Dic122C4⋊C412yes—
112C2×Dic122C2×Q811yescharacteristic
113C22⋊#6923—28no—
114C22⋊#6923—44no—
115C4⋊#6923—44no—
116C4⋊#6923—44no—
117C4×#6923—44no—
118C4×#6923—44no—
119M16×C61—41no—
120C2×C8×C61—21no—
121C2×C8×C61—21no—
122C2×C8×C61—41no—
123#11758194—41no—
124C2×#92418—21no—
125C2×#92418—21no—
126C2×#92418—41no—
127#11758189—42no—
128C8×D61—42no—
129C8×D61—41no—
130C8×D61—41no—
131C8×D61—41no—
132C8×D61—41no—
133C23×C61#9512yes—
134C23×C61C2×C4211yescharacteristic
135C22×D61—22no—
136C22×D61—21no—
137C22×D61—21no—
138C22×D61—22no—
139C22×D61—42no—
140C22×D61—44no—
141C22×D61#9511yescharacteristic
142C22×D61#9511yescharacteristic
143C22×D61C2×C22⋊C412yes—
144C2×#6923—48no—
145C2×#6923—88no—
146Q8×C61—41no—
147D4×C61—42no—
148D4×C61—41no—
149C2×C4×C61—21no—
150C2×C4×C61—21no—
151C2×C4×C61—22no—
152C2×C4×C61—22no—
153C2×C4×C61#9512yes—
154C2×C4×C61C2×C22⋊C411yescharacteristic
155C2×C4×C61C2×C4⋊C411yescharacteristic
156C22⋊D61—42no—
157C22⋊D61—42no—
158C22⋊D61—42no—
159C2×Dic61—21no—
160C2×Dic61—21no—
161C2×Dic61—22no—
162C2×Dic61—22no—
163C2×Dic61#9511yescharacteristic
164C2×Dic61#9511yescharacteristic
165C2×Dic61C2×C4⋊C412yes—
166D244—42no—
167D244—41no—
168C4×D61—21no—
169C4×D61—21no—
170C4×D61—22no—
171C4×D61—22no—
172C4×D61—21no—
173C4×D61—21no—
174C4×D61—22no—
175C4×D61—22no—
176C4×D61—22no—
177C4×D61—22no—
178C4×D61—21no—
179C4×D61—21no—
180C4×D61#9911yescharacteristic
181C4×D61#9911yescharacteristic
182C4×D61#9911yescharacteristic
183C4×D61#9911yescharacteristic
184Dic122—42no—
185Dic122—41no—
186C8×C61—41no—
187C8×C61—41no—
188#92418—41no—
189#92418—41no—
190C2×#1391—611nomaximal, Sylow
191C22×C61—22no—
192C22×C61—21no—
193C22×C61—42no—
194C22×C61—41no—
195C22×C61C2×#9511yescharacteristic
196C2×D61—22no—
197C2×D61—22no—
198C2×D61—21no—
199C2×D61—42no—
200C2×D61—44no—
201C2×D61—42no—
202C2×D61—41no—
203C2×D61—42no—
204C2×D61—82no—
205C2×D61#34211yescharacteristic
206C2×D61#34211yescharacteristic
207#6923—88no—
208C4×C61—22no—
209C4×C61—21no—
210C4×C61C2×#9911yescharacteristic
211C4×C61C2×#9911yescharacteristic
212Dic61—21no—
213Dic61—22no—
214Dic61#34211yescharacteristic
215Dic61#34211yescharacteristic
216C2×#410—612no—
217C2×#408—611no—
218#1391—612no—
219#1391—612no—
220C2×C61—21no—
221C2×C61—41no—
222C2×C61—42no—
223C2×C61C2×#34211yescharacteristic
224D61—21no—
225D61—42no—
226D61—41no—
227D61#139112yescomplemented
228C22×#41—611no—
229C22×M16—611no—
230C23×C8—611no—
231C2×#117—1222no—
232#410—614no—
233#410—614no—
234#410—1222no—
235#410—1222no—
236C2×#99—614no—
237C2×#99—1222no—
238#408—611no—
239#408—611no—
240#408—611no—
241#408—1222no—
242#408#692311yescharacteristic, complemented
243C2×C22⋊C8—1222no—
244C61C2×#139111yescharacteristic, complemented, Sylow
245C2×#41—611no—
246C2×#41—612no—
247C2×#41—611no—
248C2×#41—612no—
249C2×#41—611no—
250C2×#41—2441no—
251C2×#41—2441no—
252C2×#41—2441no—
253C2×#41—2441no—
254C2×#41C2×#692311yescharacteristic
255C22×Q8—611no—
256C22×D4—612no—
257C22×D4—611no—
258C23×C4—612no—
259C23×C4—611no—
260C2×M16—611no—
261C2×M16—1221no—
262C2×M16—2441no—
263C2×M16—2441no—
264C2×M16C2×#692311yescharacteristic, complemented
265C22×C8—611no—
266C22×C8—1221no—
267C22×C8—1221no—
268C22×C8—1221no—
269C22×C8—2441no—
270C22×C8—2441no—
271C22×C8C2×#692311yescharacteristic, complemented
272#117—1224no—
273#117—1224no—
274#117—2442no—
275#117—2442no—
276C2×C4⋊C4—2442no—
277C2×C22⋊C4—1224no—
278C2×C42—2442no—
279#99—618no—
280#99—1224no—
281#99—1224no—
282#99—1224no—
283C22⋊C8—22no—
284C22⋊C8—1222no—
285C22⋊C8—1222no—
286C22⋊C8—1222no—
287C24—612no—
288C24—611no—
289#41—41no—
290#41—41no—
291#41—2441no—
292#41—2442no—
293#41—2441no—
294#41—2442no—
295#41—2442no—
296#41—2442no—
297#41—2441no—
298#41—2441no—
299#41—2441no—
300#41—2441no—
301C2×Q8—612no—
302C2×Q8—611no—
303C2×Q8—2441no—
304C2×Q8—2441no—
305C2×Q8C4⋊#692311yescharacteristic
306C2×D4—612no—
307C2×D4—612no—
308C2×D4—612no—
309C2×D4—612no—
310C2×D4—611no—
311C2×D4—2442no—
312C2×D4—2442no—
313C2×D4—2441no—
314C2×D4—2441no—
315C2×D4C4×#692312yes—
316C2×D4C4⋊#692311yescharacteristic
317C22×C4—611no—
318C22×C4—612no—
319C22×C4—611no—
320C22×C4—612no—
321C22×C4—612no—
322C22×C4—612no—
323C22×C4—611no—
324C22×C4—611no—
325C22×C4—611no—
326C22×C4—1222no—
327C22×C4—1222no—
328C22×C4—1222no—
329C22×C4—1222no—
330C22×C4—1221no—
331C22×C4—1221no—
332C22×C4—1221no—
333C22×C4—1221no—
334C22×C4—2444no—
335C22×C4C22⋊#692312yes—
336C22×C4C22×#692311yescharacteristic
337M16—41no—
338M16—2442no—
339M16—2441no—
340C2×C8—21no—
341C2×C8—21no—
342C2×C8—41no—
343C2×C8—1221no—
344C2×C8—1221no—
345C2×C8—2441no—
346C2×C8—2441no—
347C2×C8—2441no—
348C2×C8—2441no—
349C2×C8—2442no—
350C2×C8—2441no—
351C4⋊C4—2444no—
352C4⋊C4—2444no—
353C22⋊C4—1228no—
354C22⋊C4—2444no—
355C42—2444no—
356C42—2444no—
357C23—611no—
358C23—611no—
359C23—612no—
360C23—1222no—
361C23—1222no—
362C23—1221no—
363C23—1221no—
364C23—2444no—
365C23—2442no—
366C23(C2×#6923)⋊C412yes—
367C23C2×C4×#692311yescharacteristic
368Q8—41no—
369Q8—2442no—
370Q8—2441no—
371D4—42no—
372D4—41no—
373D4—2442no—
374D4—2441no—
375D4—2442no—
376D4—2442no—
377D4—2442no—
378C2×C4—21no—
379C2×C4—22no—
380C2×C4—21no—
381C2×C4—22no—
382C2×C4—611no—
383C2×C4—611no—
384C2×C4—611no—
385C2×C4—611no—
386C2×C4—611no—
387C2×C4—611no—
388C2×C4—612no—
389C2×C4—1222no—
390C2×C4—1222no—
391C2×C4—1221no—
392C2×C4—1221no—
393C2×C4—1222no—
394C2×C4—1222no—
395C2×C4—1221no—
396C2×C4—1221no—
397C2×C4—1222no—
398C2×C4—1222no—
399C2×C4—1221no—
400C2×C4—1221no—
401C2×C4—1222no—
402C2×C4—1221no—
403C2×C4—1222no—
404C2×C4—1221no—
405C2×C4—4888no—
406C2×C4—2448no—
407C2×C4(C2×#6923)⋊C412yes—
408C2×C4C2×C22⋊#692311yescharacteristic
409C2×C4C2×C4⋊#692311yescharacteristic
410C8—41no—
411C8—41no—
412C8—2441no—
413C8—2441no—
414C22—22no—
415C22—21no—
416C22—42no—
417C22—41no—
418C22—611no—
419C22—611no—
420C22—1222no—
421C22—1222no—
422C22—1221no—
423C22—4882no—
424C22—2442no—
425C22—2441no—
426C22—2444no—
427C22—2442no—
428C22—2442no—
429C22C2×(C2×#6923)⋊C411yescharacteristic
430C4—22no—
431C4—21no—
432C4—611no—
433C4—611no—
434C4—1221no—
435C4—1222no—
436C4—4888no—
437C4D61⋊#9911yescharacteristic
438C4D61⋊#9911yescharacteristic
439C2—21no—
440C2—42no—
441C2—41no—
442C2—612no—
443C2—1221no—
444C2—2442no—
445C2—2441no—
446C2#2146151611yescharacteristic
subgroupG/H
centerC4D61⋊#99
commutatorC23×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC61×#408C4
socleC2×C61C2×#342
prime radicalC2×#41×D61C22
cosocleC2×#11758222C23
hypercenter#408#6923
hypocenterC61C2×#1391
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #408

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #21460908C2semidirect
3. #21460907C2semidirect
7. #16840742C4semidirect
11. D61⋊#99C4semidirect
13. C2×M16×D61C4semidirect
14. C22×C8×D61C4semidirect
16. #16839729C4semidirect
20. C61×#408C4semidirect
31. #14519835C2×C4semidirect
46. C2×#11758194C2×C4semidirect
50. C22×#92418C2×C4semidirect
60. C2×M16×C61C2×C4semidirect
61. C22×C8×C61C2×C4semidirect
227. D61#1391semidirect
242. #408#6923semidirect
244. C61C2×#1391semidirect
264. C2×M16C2×#6923semidirect
271. C22×C8C2×#6923semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
D61⋊#4102
#214609082
#214609072
#408×D612
C2×#139161